pcfdot: Multitype pair correlation function (i-to-any)

In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

Multitype pair correlation function (i-to-any)

Description

Calculates an estimate of the multitype pair correlation function (from points of type i to points of any type) for a multitype point pattern.

Usage

  pcfdot(X, i, ...)

Arguments

X	The observed point pattern, from which an estimate of the dot-type pair correlation function g_{i\bullet}(r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor).
i	The type (mark value) of the points in X from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of marks(X).
...	Arguments passed to pcfmulti to control the computation.

Details

This is a generalisation of the pair correlation function pcf to multitype point patterns.

For two locations x and y separated by a nonzero distance r, the probability p(r) of finding a point of type i at location x and a point of any type at location y is

p(r) = \lambda_i \lambda g_{i\bullet}(r) \,{\rm d}x \, {\rm d}y

where \lambda is the intensity of all points, and \lambda_i is the intensity of the points of type i. For a completely random Poisson marked point process, p(r) = \lambda_i \lambda so g_{i\bullet}(r) = 1.

For a stationary multitype point process, the type-i-to-any-type pair correlation function between marks i and j is formally defined as

g_{i\bullet}(r) = \frac{K_{i\bullet}^\prime(r)}{2\pi r}

where K_{i\bullet}^\prime is the derivative of the type-i-to-any-type K function K_{i\bullet}(r). of the point process. See Kdot for information about K_{i\bullet}(r).

The command pcfdot computes a kernel estimate of the multitype pair correlation function from points of type i to points of any type.

The companion function pcfcross computes the corresponding analogue of Kcross.

Value

An object of class "fv", see fv.object, which can be plotted directly using plot.fv.

Essentially a data frame containing columns

r	the vector of values of the argument r at which the function g_{i\bullet} has been estimated
theo	the theoretical value g_{i\bullet}(r) = 1 for independent marks.

together with columns named "border", "bord.modif", "iso" and/or "trans", according to the selected edge corrections. These columns contain estimates of the function g_{i,j} obtained by the edge corrections named.

Author(s)

\adrian

and \rolf

See Also

Mark connection function markconnect.

Multitype pair correlation pcfcross, pcfmulti.

Pair correlation pcf,pcf.ppp.

Kdot

Examples

 p <- pcfdot(amacrine, "on")
 p <- pcfdot(amacrine, "on", stoyan=0.1)
 plot(p)

spatstat.explore documentation built on March 22, 2026, 5:06 p.m.